arrow
arrow
arrow
What is the number of natural numbers less than or equal to 1000 and divisible by 5 or 7?
Question

What is the number of natural numbers less than or equal to 1000 and divisible by 5 or 7?

A.

314

B.

328

C.

342

D.

370

Correct option is A

Given:
Range: Natural numbers less than or equal to 1000
Divisors: 5 or 7
Formula Used:
​n(A∪B)=n(A)+n(B)−n(A∩B)n(A \cup B) = n(A) + n(B) - n(A \cap B)​​
Solution:
Number of terms divisible by 5 = ⌊10005⌋=200 \lfloor \frac{1000}{5} \rfloor = 200​​

Number of terms divisible by 7 = ⌊10007⌋=142 \lfloor \frac{1000}{7} \rfloor = 142​​
Number of terms divisible by both 5 and 7 (i.e., 35) = ⌊100035⌋=28\lfloor \frac{1000}{35} \rfloor = 28​​
Total numbers divisible by 5 or 7 = 200 + 142 - 28
Total numbers = 342 - 28 = 314
Final Answer
So the correct answer is (a)

Free Tests

Free
Must Attempt

RRB NTPC UG Level PYP (Held on 7 Aug 2025 S1)

languageIcon English
  • pdpQsnIcon100 Questions
  • pdpsheetsIcon100 Marks
  • timerIcon90 Mins
languageIcon English
Free
Must Attempt

CBT-1 Full Mock Test 1

languageIcon English
  • pdpQsnIcon100 Questions
  • pdpsheetsIcon100 Marks
  • timerIcon90 Mins
languageIcon English
Free
Must Attempt

RRB Group D Full Mock Test 1

languageIcon English
  • pdpQsnIcon100 Questions
  • pdpsheetsIcon100 Marks
  • timerIcon90 Mins
languageIcon English
test-prime-package

Access ‘RRB Group D’ Mock Tests with

  • 60000+ Mocks and Previous Year Papers
  • Unlimited Re-Attempts
  • Personalised Report Card
  • 500% Refund on Final Selection
  • Largest Community
students-icon
564k+ students have already unlocked exclusive benefits with Test Prime!
Our Plans
Monthsup-arrow